Growing American Shipping Act of 2014 - Amends the Coast Guard and Maritime Transportation Act of 2006 to expand the directive to the Department of Transportation (DOT) to develop and implement a program to promote the transportation of imports of liquefied natural gas to the United States on U.S.-flag vessels to include the promotion of the transportation of exports of the gas from the United States.
Amends the Deepwater Port Act of 1974 to require DOT to give top priority to the processing of a license for liquefied natural gas facilities at a deepwater port that will supply the gas to be exported on U.S.-flag vessels in addition to the priority currently given to the processing of licenses for imports of the gas.